`((1001)_(2)^((11)_(2)) - (101)_(2)^((11)_(2)))/((1001)_(2)^((10)_(2)) + (1001)_(2)^((01)_(2)) * (101)_(2)^((01)_(2)) + (101)_(2)^((10)_(2))) ` का मान क्या है ?

Options

A. `(1001)_(2)`
B. `(101)_(2)`
C. `(110)_(2)`
D. `(100)_(2)`

Answer

d

Explanation

`because (1001)_(2) = 1 xx 2^(3) + 0 xx 2^(2) + 0 xx 2^(1) + 1 xx 2^(0) = 8 + 1 = 9 `
`(11)_(2) = 2^(1) xx 1 + 2^(0) xx 1 = 2 + 1 = 3`
`(101)_(2) = 1 xx 2^(2) + 0 xx 2^(1) + 1 xx 2^(0) = 4 + 1 = 5`
`(10)_(2) = 2^(1) xx 1 + 2^(0) xx 0 = 2 + 0 = 2`
तथा `(01)_(2) = 0 xx 2^(1) + 1 xx 2^(0) = 1`
`((1001)_(2)^((11)_(2)) - (101)_(2)^((11)_(2)))/((1001)_(2)^((10)_(2)) + (1001)_(2)^((01)_(2)) * (101)_(2)^((01)_(2)) + (101)_(2)^((10)_(2))) `
`= ((9)^(3) - (5)^(3))/((9)^(2) + 9 xx 5 + (5)^(2))`
`((9-5) (9^(2) + 9 xx 5 + 5^(2)))/((9^(2) + 9 xx 5 + 5^(2)))`
`= 9 - 5 = 4 = (100)_(2)`